Question: Simplify; express your answer in exponential form. Assume $n\neq 0, x\neq 0$. $\dfrac{{(n^{3}x^{-3})^{-2}}}{{(n^{-4}x^{-5})^{4}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(n^{3}x^{-3})^{-2} = (n^{3})^{-2}(x^{-3})^{-2}}$ On the left, we have ${n^{3}}$ to the exponent ${-2}$ . Now ${3 \times -2 = -6}$ , so ${(n^{3})^{-2} = n^{-6}}$ Apply the ideas above to simplify the equation. $\dfrac{{(n^{3}x^{-3})^{-2}}}{{(n^{-4}x^{-5})^{4}}} = \dfrac{{n^{-6}x^{6}}}{{n^{-16}x^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-6}x^{6}}}{{n^{-16}x^{-20}}} = \dfrac{{n^{-6}}}{{n^{-16}}} \cdot \dfrac{{x^{6}}}{{x^{-20}}} = n^{{-6} - {(-16)}} \cdot x^{{6} - {(-20)}} = n^{10}x^{26}$